Solve the following equation:
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Solve the following equation:
Let's first identify the lowest common denominator between 10 and 12.
In order to determine the lowest common denominator, we need to find a number that is divisible by both 10 and 12.
In this case, the common denominator is 60.
We'll proceed to multiply each fraction by the appropriate number to reach the denominator 60.
We'll multiply the first fraction by 6
We'll multiply the second fraction by 5
Now let's add:
Without calculating, determine whether the quotient in the division exercise is less than 1 or not:
\( 5:6= \)
You can't add fractions with different denominators because they represent parts of different-sized wholes. It's like trying to add 4 slices of a 10-piece pizza to 5 slices of a 12-piece pizza - you need a common reference first!
List the multiples of each number: 10: 10, 20, 30, 40, 50, 60... 12: 12, 24, 36, 48, 60... The first number that appears in both lists is 60, so that's your LCD!
Divide the LCD by each denominator: 60 ÷ 10 = 6 and 60 ÷ 12 = 5. So multiply the first fraction by 6/6 and the second by 5/5.
No! Since 49 = 7 × 7 and 60 = 2² × 3 × 5, they share no common factors. The fraction is already in lowest terms.
While 120 works (it's divisible by both 10 and 12), it's not the least common denominator. You'd get , which simplifies back to anyway!
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